Airy Gaussian Research Articles

Observation of the rotational Doppler shift of the ring Airy Gaussian vortex beam

We observe the rotational Doppler shift of an orbital angular momentum-carrying ring Airy Gaussian vortex (RAiGV) beam based on the rotational Doppler effect (RDE) for the first time. The Airy Gaussian beam has attracted a considerable interest in recent years owing to its autofocusing characteristics which indicates an important potential use in optical trapping. Here we propose a scheme for spinning object detection by employing such a RAiGV beam. The RAiGV beam is prepared by a spatial light modulator. An experiment scheme is proposed in a superposition light system, and the results show that the RAiGV has the same well performance in spinning speed detection with other optical vortex beams. It is also found that by varying the scale factor and ring radius of the RAiGV beam, the intensity profile varies accordingly, as well as the autofocusing distance. Especially, we find that a larger scale factor leads to a higher SNR, while as the ring radius changes, the signals are almost not affected. Furthermore, the RDE signal can be recognized with high accuracy even at the autofocusing position, which is confirmed through repeating the measurement along the propagation path of the RAiGV beam. The results of this work may find useful applications in Doppler velocimetry, remote sensing and metrology.

Generating arbitrary arrays of circular Airy Gaussian vortex beams with a single digital hologram

Circular Airy Gaussian vortex (CAGV) beams have gained great popularity in areas of research such as optical tweezers and optical communications due to their fascinating properties, such as auto-focusing and self-healing. The propagation dynamics of these beams is dictated by their topological charge and launch angle. For example, larger topological charges and positive launch angles enhance the maximum intensity in the focal plane while simultaneously shortening the focal length of autofocusing. Crucially, while the generation of single CAGV beams has been widely reported, the simultaneous generation of multiple CAGV beams, has remained challenging. Here, we put forward a novel technique that enables the simultaneous generation of multiple CAGV beams with independent topological charges or initial launch angles from a single digital hologram encoded on a spatial light modulator (SLM). Our technique enables the independent manipulation of each CAGV beam, their topological charge and launch angle, at refresh rates limited only by the SLM (60 Hz). This technique paves the way for the simultaneous manipulation of microparticles in three dimensions and provides with an alternative way to realize optical communications with multiple spatial modes of light.

Tight-Focusing Properties of the Chirp Modulation Linearly Polarized Circular Airy Gaussian Vortex Beam

Tight-Focusing Properties of the Chirp Modulation Linearly Polarized Circular Airy Gaussian Vortex Beam

Propagation dynamics of abruptly autofocusing circular Airy Gaussian vortex beams in the fractional Schrödinger equation

We have investigated the propagation dynamics of the circular Airy Gaussian vortex beams (CAGVBs) in a (2+1)-dimesional optical system discribed by fractional nonlinear Schr\"odinger equation (FNSE). By combining fractional diffraction with nonlinear effects, the abruptly autofocusing effect becomes weaker, the radius of the focusing beams becomes bigger and the autofocusing length will be shorter with increase of fractional diffraction L\'evy index. It has been found that the abruptly autofocusing effect becomes weaker and the abruptly autofocusing length becomes longer if distribution factor of CAGVBs increases for fixing the L\'evy index. The roles of the input power and the topological charge in determining the autofocusing properties are also discussed. Then, we have found the CAGVBs with outward acceleration and shown the autodefocusing properties. Finally, the off-axis CAGVBs with positive vortex pairs in the FNSE optical system have shown interesting features during propagation.

Propagation properties and radiation force of circular Airy Gaussian vortex beams in strongly nonlocal nonlinear medium* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108 and 11775083).

We study the abruptly autofocusing and autodefocusing properties of the circular Airy Gaussian vortex (CAiGV) beams in strongly nonlocal nonlinear medium for the first time through numerical simulations. The magnitude of topological charges and the position of the vortex could change not only the light spot pattern but also the intensity contrast. Meanwhile, we can change the position of the autofocusing and autodefocusing planes by changing the parameter of the incident beam. Furthermore, we can control the peak intensity contrast through choosing properly the truncation factor. As for the radiation force, we study the gradient and the scattering forces of CAiGV beams on Rayleigh dielectric sphere. Our analyses demonstrate that the radiation force can be enhanced by choosing proper parameters of CAiGV beams.

Transversely polarized ultra-long optical needles generated by cylindrical polarized circular airy gaussian vortex beams

We theoretically demonstrate a transversely polarized ultra-long optical needle with lateral width beyond diffraction limit generated by tight focusing of a cylindrical polarized circular Airy Gaussian vortex beam (CAiGVB). According to the calculation expression derived through the Richard–Wolf​ diffraction theory, the properties of optical needles are investigated in simulation in detail. The analysis reveals that the interaction between the vortex phase and the state of polarization of the CAiGVB through tight focusing results in the generation of the transversely polarized optical needles. The depth of the optical needle is strongly affected by the maximum position of the brightest ring, the optical distribution factor and the truncation factor of the CAiGVB. However, the lateral width of optical needle is only influenced by the maximum position of the brightest ring. The simulation results indicate that an optical needle of longitudinal length 38λ with lateral width of only 0.46λ can be achieved. To improve the intensity uniformity of longitudinal direction, a method of the combination of tight focusing with a binary phase element is used Such a transversely polarized optical needle has significant potential in atomic trapping and ultrahigh density magnetic storage.

Domains of modulation parameter in the interaction of finite Airy–Gaussian laser beams with plasma

AbstractIn this paper, self-focusing of finite Airy–Gaussian (AiG) laser beams in collisionless plasma has been investigated. The source of nonlinearity considered herein is relativistic. Based on the Wentzel–Kramers–Brillouin (WKB) and paraxial-ray approximations, the nonlinear coupled differential equations for beam-width parameters in transverse dimensions of AiG beams have been established. The effect of beam's modulation parameter and linear absorption coefficient on the self-focusing/defocusing of the beams is specifically considered. It is found that self-focusing/defocusing of finite AiG beams depends on the range of modulation parameter. The extent of self-focusing is found to decrease with increase in absorption.

Airy Beam for Free-Space Photonic Interconnection: Generation Strategy and Trajectory Manipulation

Self-accelerating beams have attracted worldwide research attentions due to their intriguingly curved trajectory with localized peak intensity and the characteristic of self-healing after obstacles. We first put forward a generation vector to analytically describe general trajectory manipulation for 2-D Airy beam. Based on the successful trajectory manipulation of 2-D Airy beam, a 100 Gbps NRZ-OOK real-time free-space photonic interconnection is experimentally demonstrated. Our results indicate that the bending trajectory can break the constraints of traditional free-space photonic interconnection where the receiver has to be set under the condition of line-of-sight. Meanwhile, by taking the power correction factor into account of the beam width variation, we propose a metric of normalized power density (NPD) in order to characterize the power density variation of beam main lobe along the free-space propagation. After calculating the 3 dB NPD range of both Airy beam and Gaussian beam, we identify that the power density of Airy beam main lobe can be maintained for a longer free-space reach than a Gaussian beam with the same minimum width.

Propagation properties of the chirped Airy–Gaussian vortex electron plasma wave* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11775083 and 11374108), the Science and Technology Program of Guangzhou City (Grant No. 2019050001), and the Special Funds for the Cultivation of Guangdong College Students' Scientific and Technological Innovation (Grant Nos. pdjh2020a0149 and pdjh2019a0127).

We introduce a new class of the chirped Airy–Gaussian vortex electron plasma (CAiGVEP) wave which constitutes the exact and continuous transition modes between the chirped Airy vortex and the chirped Gaussian vortex electron plasma wave. The intensity, the phase, and the angular momentum density flow of the CAiGVEP wave are discussed under different distribution factors and different chirp modes.

Tight-focusing properties of radially polarized chirped circular Airy Gaussian beam

We investigate the tight-focusing properties of radially polarized chirped circular Airy Gaussian beam (RPCCAiGB) based on the Richards–Wolf vectorial diffraction theory. The RPCCAiGB propagating through a high numerical aperture objective lens enables the intensity of the longitudinal component to surpass the intensity of the radial component. The focal length, the focused intensity and the radiation forces of the RPCCAiGB are tunable by setting different optical distribution factors and radii of the primary ring. The chirped parameter influences the magnitude of radiation forces and enables an access to the desired focal position of the beam. These results can be potentially applied to many aspects, such as optical communication, optical trapping and medical treatment.

Off‐Axis and Multi Optical Bottles from the Ring Airy Gaussian Vortex Beam with the Astigmatic Phase

AbstractA new type of off‐axis and multi optical bottle (OB) from an astigmatic‐phase ring Airy Gaussian vortex beam (APRAGVB) propagating in free space is derived numerically. By choosing appropriate parameters, different sizes and amounts of OBs can be obtained. More importantly, when the APRAGVB has the multi optical vortices at different locations, one can generate off‐axis, multi, and complex OBs. It is believed that the results can diversify optical tweezers applications for multi microparticle manipulation.

Ring Airy‐Like Beams along Predesigned Parabolic Trajectories

AbstractBy phase‐modulating ring Airy Gaussian beams, ring Airy‐like beams propagating along predesigned parabolic trajectories are presented which combine the properties of accelerating beams and abruptly autofocusing beams analytically and numerically for the first time. The enhancement of the quadratic term ratio α shortens the autofocus distance and increases the slope of the beams after autofocusing. Interestingly, the main lobe tends to break into pieces as α increases and the possible reasons have been discussed. Furthermore, the distribution factor β and the radius of the primary r0 can prominently affect the autofocus distance and the intensity at the focal point but do not change the slope of the beams after the autofocusing. In addition, the self‐healing properties are validated to be retainable while RAiG beams via predesigned parabolic trajectories with various α.

Mechanism of two-dimensional finite airy gaussian array beams through curved slab systems

Combining the ABCD transfer matrix and the generalised Huygens-Fresnel integral equation method, the closed-form expression of a finite Airy Gaussian array beam (FAGAB) threading through a paraxial optical system was established in a space domain. We systematically investigated the evolution of the FAGAB's properties travelling through a curved slab system based on previously derived formula. The wave's characteristics through the flat slab system were the special cases of the main findings. We also assess the influence of the truncation factor and adjustment parameter on the FAGAB's intensity distribution on the slab system model's input and output cross-sections.

Coherent interactions of multi-Airy–Gaussian beams in photorefractive media

We have investigated the interaction properties of multi-Airy-Gaussian beams under the in-phase and out-phase conditions, respectively. For the case of three Airy–Gaussian beams, the breathing solitons with single, two and three components can be observed under certain conditions. The breathing solitons with single, three and four components can be observed for four Airy–Gaussian beams. The types of breathing solitons for out-phase multi-Airy–Gaussian beams are less than that of in-phase multi-Airy–Gaussian beams. Furthermore, the types of breathing solitons can be controlled by adjusting the space interval, nonlinear parameter and self-accelerating direction.

Propagation of the Pearcey Gaussian beams in a medium with a parabolic refractive index

We have studied the propagation of the Pearcey Gaussian (PeG) beams in a medium with a parabolic refractive index. Compared to the Airy Gaussian beams and common Gaussian beams, there occur two kinds of focusing when the PeG beams propagate in a medium with a parabolic refractive index. One is the auto-focusing caused by the PeG beams and the other is the focusing effect for which the parabolic refractive index is responsible. In addition, we also have made a comparison of the focus-ability between these two kinds of focusing by analyzing the mean-squared beam width and the power in the bucket.

Effect of Airy Gaussian vortex beam array on reducing intermode crosstalk induced by atmospheric turbulence.

Vortex beam carrying angular momentum (OAM) will be disturbed by the random fluctuation of the refraction index of turbulent atmosphere, resulting in intermodal crosstalk among the different OAM modes. Recent advances have demonstrated that the employment of the abruptly autofocusing vortex beams can potentially mitigate the crosstalk effect. In this paper, a new type of abruptly autofocusing vortex beams, called Airy Gaussian vortex beam array (AGVBA) is proposed. By means of multi-plane wave optics simulation, the degradation of signal mode for AGVBA propagating through isotropic atmospheric turbulence is studied. In a comparison with the conventional abruptly autofocusing vortex beams, such as the ring Airy vortex beam (RAVB) and the Airy vortex beam array (AVBA), it is shown that AGVBA achieves more centralized intensity as well as a larger spot at the focal plane, thus can effectively balance the beam spreading and beam wander effect, resulting in mitigation of intermodal crosstalk.

Periodic propagation of radially and azimuthally polarized first-order chirped Airy Gaussian beams in a harmonic potential

By solving the (2 + 1) D Schrödinger equation with an external harmonic potential, the expressions for the radially and azimuthally polarized first-order chirped Airy Gaussian beams (RPCAiG beams and APCAiG beams) propagating in a harmonic potential are deduced. The simulation results display that the intensities of the RPCAiG beams and APCAiG beams, which exhibit periodic inversion and oscillation propagation, can be adjusted in the x-direction and the y-direction by changing the distribution factors βx and βy. Besides, by selecting negative or positive chirped parameters cx and cy, we can obtain decelerating or accelerating the beams in the x-direction and the y-direction, respectively. Furthermore, the gradient force, the maximum scattering force, the Poynting vector and angular momentum of both beams have been investigated.

Bound states of chirped Airy–Gaussian beams in a medium with a parabolic potential

Starting from the normalized dimensionless linear parabolic (Schrodinger-like) equation, by means of split-step Fourier numerical simulation, in this paper we investigate the interaction between two chirped Airy–Gaussian (CAiG) beams in a medium with a parabolic potential. We find that a parabolic potential provides interesting effects and supports the bound states of two CAiG beams. We also study the effect of chirps and found that large enough chirps will weaken the energy of bound states. Moreover, initial parameters of the beams, initial interval, amplitudes, and distribution factor, are taken into consideration as well.

Propagation of cosine complex variable function Airy–Gaussian beams through the gradient-index medium

We introduce a new class of cosine complex variable function Airy–Gaussian (Cos-CVFAiG) beams and investigate their propagation through the gradient-index medium. Deriving the analytical expression, we show the intensity and phase distributions, the propagation trajectory and the Poynting vector. We carry out the numerical experiment to verify the rationality of the model and find that the light intensity distribution is parallel to the y axis in the transverse plane. With the distribution factor increasing, the axial intensity maximum and the number of the side lobes increase as well. Additionally, the distribution factor can change the bend extent of the ballistic trajectory and the intensity distribution region in the x–z plane. We also compare the influences of the gradient refractive index coefficient with the distribution factor on the propagation properties.

Propagation properties of chirped Airy hollow Gaussian wave packets

Abstract Based on the analytic expression of the chirped Airy hollow Gaussian (CAiHG) wave packets derived from the ( 3 + 1 )-dimensional ( ( 3 + 1 ) D) Schrodinger equation, their propagation properties are investigated in detail for the first time. The results show that a focusing of the chirped Airy Gaussian pulses is found, which leads to the same focusing of the propagation trajectory and the maximum scattering force. The distribution factor α can modulate the convergence of the side wave rings at Z = 0 . During the propagation process, with the increase of the β , when the β is negative, the side wave rings rise along the main wave axis but their moving is opposite when the β is positive. When the beam order n = 1 , the intensity, the angular momentum and the gradient force gradually tend to the center but they move radially when n = 2 . The direction of the peripheral gradient force points to the center but the direction is opposite in the center. The beam orders only affect the magnitude of the normalized maximum scattering force but have little effects on their distribution.